Renormalisation of the Fayet-Iliopoulos D-term

We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken Abelian supersymmetric theory. We show that there exists (at least through three loops) a renormalisation group invariant trajectory for the coefficient of the D-term, corresponding to the conformal anomaly solution for the soft masses and couplings.Comment: 11 pages, TeX, Uses Harvmac (big). References added, minor corrections (including a sign error for the zeta(3) terms), and discussion of scheme dependence corrected and amplifie

Anomaly Mediation and Dimensional Transmutation

We show how a sparticle spectrum characteristic of anomaly mediation can arise from a theory whose Lagrangian contains no explicit mass scale. The scale of supersymmetry breaking is governed by the gravitino mass, which is the vacuum expectation value of the F-term of the conformal compensator field, and the tachyonic slepton problem is resolved by the breaking of a U(1) gauge symmetry at a scale determined by dimensional transmutation.Comment: 12 pages, 1 figure. v2 has added preprint number and acknowledgement

Asymptotic Pad\'e Approximants and the SQCD β\beta-function

We present a prediction for the four loop $\beta$-function for SQCD based on the method of Asymptotic Pad\'e Approximants.Comment: 8 pages, including 2 figures. Plain TeX. Uses Harvmac and eps

Gauge singlet renormalisation in softly-broken supersymmetric theories

We consider the renormalisation of a softly-broken supersymmetric theory with singlet fields and a superpotential with a linear term. We show that there exist exact beta-functions for both the linear term in the superpotential and the associated linear term in the Lagrangian. We also construct exact renormalisation group invariant trajectories for these terms, corresponding to the conformal anomaly solution for the soft masses and couplings.Comment: 13 pages, Plain TeX, uses Harvmac. Typos corrected and minor clarification adde

Yukawa Textures and the mu-term

We show how with an anomaly-free U(1), simple assumptions concerning the origin of Yukawa textures and the Higgs mu-term lead to the prediction of a new physics scale of 10^8GeV and automatic conservation of baryon number.Comment: 12 pages, uses Harvmac (option "b"

The connection between the DRED and NSVZ renormalisation schemes

We explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $\beta$-function, we derive the transformation of \alpha^{\DRED} to \alpha^{\NSVZ} through terms of order $\alpha^4$. We thus incidentally determine \beta_{\alpha}^{\DRED} through four loops, and we compare our result to a previous Pad\'e Approximant prediction.Comment: 9 pages, including 1 figure. Plain TeX. Uses Harvmac and epsf. Version to be published in Phys. Lett. B. with minor corrections (and modified title

Two-loop beta-functions and their effects for the R-parity Violating MSSM

We present the full two-loop beta-functions for the MSSM including R-parity violating couplings. We analyse the effect of two-loop running on the bounds on R-parity violating couplings, on the nature of the LSP and on the stop masses.Comment: 12 pages, including 2 figures. Plain TeX. Uses Harvmac and epsf. Revised version with corrected Table and Figure

Snowmass Benchmark Points and Three-Loop Running

We present the full three-loop beta-functions for the MSSM generalised to include additional matter multiplets in 5, 10 representations of SU(5). We analyse in detail the effect of three-loop running on the sparticle spectrum for the MSSM Snowmass Benchmark Points. We also consider the effect on these spectra of additional matter multiplets (the semi-perturbative unification scenario).Comment: 28 pages, TeX, 4 figures, 10 tables. Uses Harvmac and eps

Three loop soft running, benchmark points and semi-perturbative unification

We consider three-loop $\beta$-function corrections to the sparticle spectrum in the MSSM, with particular emphasis on Snowmass Benchmark points. The three loop running has little effect on the weakly interacting particle spectrum, but for the squark masses the effect can be comparable to, or greater than, that of two loop running. We extend the analysis to the semi-perturbative unification scenario, where the impact of the three loop corrections becomes even more dramatic.Comment: 12 pages, TeX, Uses Harvmac (big) and epsf. Added references (v2). More emphasis on magnitude of three loop corrections (v3

R-parity Violation and General Soft Supersymmetry Breaking

We consider the most general class possible of soft supersymmetry breaking terms that can be added to the MSSM, with and without R-parity violation, consistent with the sole requirement that no quadratic divergences are induced. We renormalise the resulting theory through one loop and give an example of how a previously ignored term might affect the sparticle spectrum.Comment: 11 pages, 1 figure. Plain TeX, uses Harvmac (Big) and epsf. Added references and typo corrected (v2